But the former UK foreign secretary believes in an EU with different tiers of membership.
In London, UK Foreign Secretary William Hague said the continuing violence was "deplorable and must stop".
Mr Lavrov is due to visit London next week for talks with UK Foreign Secretary William Hague.
She is due to meet William Hague - the first UK foreign secretary to visit since 1955.
They were later joined by UK Foreign Secretary Jack Straw, and the mayor of Toulouse Philippe Douste-Blazy.
Earlier, UK Foreign Secretary William Hague said the Friends of Syria were determined to "ramp up" assistance to the opposition.
Mr Rammell - and UK foreign secretary David Miliband - have since confirmed that this report was accurate.
Mr Miliband, a politician and former UK foreign secretary, said the club had been honoured to be chosen.
As the former UK Foreign Secretary David Miliband said, "the antidote to European scepticism is founded on youth delivery".
The meeting was designed, as UK Foreign Secretary David Miliband put it, to "restart UN engagement on this issue".
When the UK Foreign Secretary, Jack Straw, went to Gibraltar, he was booed by demonstrators shouting "traitor" and "Judas".
Mr Straw, the first UK foreign secretary to visit Tehran since the 1979 Islamic revolution, will also discuss bilateral relations.
Former UK Foreign Secretary Robin Cook, who quit over the issue of war against Iraq, has also re-entered the debate.
"There are voices always from all sides who say that certain things are wrong, " says UK Foreign Secretary Jack Straw.
Meanwhile UK Foreign Secretary William Hague reiterated that Syria must allow access to a UN team to investigate the chemical weapons claims.
"Britain's policy couldn't remain static in the face of an ever-deteriorating situation, " said the UK Foreign Secretary William Hague as he left the meeting.
On Friday, UK Foreign Secretary Jack Straw said the UK would reject the draft if it meant states would lose their veto over foreign policy.
The UK Foreign Secretary, Jack Straw, has arrived in Iran on a visit aimed to explore how Iran can help with the international campaign against terrorism.
Addressing the Friends of Syria meeting, UK Foreign Secretary William Hague said on Wednesday that the UK did "not rule out any option to save lives".
She said Ecuador was "waiting for a meeting" with either UK Foreign Secretary William Hague or UK Home Secretary Theresa May to discuss Mr Assange's future.
Also on Monday, UK Foreign Secretary William Hague arrived in the Malian capital, Bamako, to hold talks with the Malian government and commanders of the African-led intervention force.
BBC: Islamist commander Abou Zeid's death in Mali 'probable'
She gave her backing to Argentina's ambassador in London, Alicia Castro, who on Monday asked UK Foreign Secretary William Hague to "give peace a chance" by opening dialogue.
BBC: Falklands tension: Argentina marks Belgrano anniversary
He said he had yet to receive a reply to a letter he wrote to UK Foreign Secretary Jack Straw four weeks ago on behalf of the British detainees.
Speaking on Thursday, UK Foreign Secretary William Hague said he would be "very surprised" if Afghan forces had not taken control of their own security from international forces by 2014.
Speaking on the BBC's Andrew Mar programme, the UK foreign secretary called on the US to show "necessary leadership" in the coming months because of its "crucial leverage with Israel", he said.
Earlier, UK Foreign Secretary Jack Straw told MPs that a failure to endorse a deadline in Tuesday's session "can only bring comfort to tyrants and emasculate the authority of the United Nations".
Rice was accompanied by her UK counterpart, Foreign Secretary Jack Straw, who is a local member of Parliament.
The UK's Foreign Secretary William Hague said the attack had "shocked Pakistan and the world" and that Malala's bravery was "an example to us all".
Mr Ritter's critics - including the UK Foreign Office and US Secretary of State Madeleine Albright - say he cannot see the wider political context.
Azer Khalilov said his brother had written 15 letters to UK Prime Minister Gordon Brown and Foreign Secretary David Miliband, but that these letters had not been received by the British consul in Bishkek.
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